Question

Please help me, I'm having a hard time understanding this question...
(Consider the point P(-2,3) and the line defined by 2x+3y=12)
1. Give the Equation of the line (in slope-intercept form) through P and parallel to the given line.

2, give the equation (in slope intercept form) of the line through P and perpendicular to the given line.

Answer 1

"Give the Equation of the line (in slope-intercept form) through P and parallel to the given line."

Parallel lines have the same slope. So, find the slope of the given line. Then use it and the given point to find the equation of the new line.

You could use any of the three main equations for a straight line: point-slope, slope-intercept or standard form equation (which is what you were given).

Hope this helps.

Answer 2

so the slope is 2... but I don't know how to find the rest? Is the slope also the same for perpendicular lines?

Answer 3

There's another way, although y ou won't find it in most books.

If you have the equation 2x+3y=12 and want to find the eq'n of a parallel line passing thru P(-2,3), do this: Drop the 12. substitute -2 for x in 2x+3y=12 and 3 for y. Calculate the constant. Done.